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This paper presents a novel algorithm and sensor for localization of a magnetic dipole. We show that the azimuth angle of the dipole can be uniquely and directly determined from the first order Fourier coefficients of the magnetic field on a circle with an arbitrary radius centered at the origin. Then, we develop two coils which directly measure the first order Fourier coefficients of the magnetic field. The proposed method is verified by a crack detection experiment using the leakage magnetic flux method.